91Ó°ÊÓ

When dealing with negative numbers, it's important to understand how they interact in different mathematical operations. In division, the rule to remember is:

- A negative number divided by a positive number results in a negative quotient.

- A positive number divided by a negative number also results in a negative quotient.

- A negative number divided by another negative number results in a positive quotient.

Let’s apply this to our problem. We are dividing -6.305 by -0.13. According to the rules, dividing two negative numbers will give us a positive quotient.

Next, let's discuss decimal division. Dividing numbers with decimals can seem tricky, but it's manageable by following a few steps:

1. **Identify the scale of decimals:** In our problem, -6.305 and -0.13 have three and two decimal places, respectively.

2. **Shift the decimal point:** To simplify division, we shift the decimal points in both the dividend (numerator) and the divisor (denominator) to the right until the divisor is a whole number.

For example, in our problem, shifting the decimal point two places to the right for both numbers, transforms the operation to 630.5 divided by 13.

3. **Divide normally:** Finally, divide the numbers as you would with whole numbers. In our case, \[ \frac{630.5}{13} = 48.5 \].

This approach makes it easier to see and perform the division.

The quotient is the result you get when one number is divided by another. In mathematical terms, if you have a dividend \(A\) and a divisor \(B\), the quotient \(Q\) is found by \[(Q = \frac{A}{B})\].

In our example problem, we've established how to handle the signs and the decimals. Now, by dividing 630.5 by 13, we achieve our quotient:

48.5.

Remember,

• The quotient tells you how many times the divisor fits into the dividend.
• It indicates whether the division was exact, showing the remainder if there's any.
• With negative numbers, adjusting signs is crucial to find the correct, positive, or negative quotient.

By understanding quotients through these steps, you can solve various division problems with confidence!